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We describe laboratory experiments of granular material flowing over an inclined plane covered by an erodible bed, designed to mimic erosion processes of natural flows travelling over deposits built up by earlier events. Two controlling parameters are the inclination of the plane and the thickness of the erodible layer. We show that erosion processes can increase the flow mobility (i.e., runout) over slopes with inclination close to the repose angle of the grains θr by up to 40%, even for very thin erodible beds. Erosion efficiency is shown to strongly depend on the slope of the topography. Entrainment begins to affect the flow at inclination angles exceeding a critical angle θc ≃ θr/2. Runout distance increases almost linearly as a function of the thickness of the erodible bed, suggesting that erosion is mainly supply-dependent. Two regimes are observed during granular collapse: a first spreading phase with high velocity followed by a slow thin flow, provided either the slope or the thickness of the erodible bed is high enough. Surprisingly, erosion affects the flow mostly during the deceleration phase and the slow regime. The avalanche excavates the erodible layer immediately at the flow front. Waves are observed behind the front that help to remove grains from the erodible bed. Steep frontal surges are seen at high inclination angles over both rigid or erodible bed. Finally, simple scaling laws are proposed making it possible to obtain a first estimate of the deposit and emplacement time of a granular collapse over a rigid or erodible inclined bed.